Reading Ma 2004 Chapter 5

Briefing Relative Pose Lecture

Exercises

Exercise 5.5

Explain under what conditions the family of epipolar lines in at least one of the image planes will be parallel to each other. Where is the corresponding epipole (in terms of is homogeneous co-ordinates)?

To make sense of the question, you have two draw the situation.

1. Draw the two origins and the two image planes. Where are the epipoles?
2. Draw two or three separate object points (3D) and the corresponding epipolar planes. (Avoid object points in the same epipolar plane.) Where are the corresponding epipolar lines?
3. If you have now identified different epipolar planes within one fixed camera configuration, you will have a family of epipolar lines in each image plane. Where do these lines intersect?
4. Try to rotate one of the cameras.
   • Can you rotate it so that the epipolar lines become parallel?
   • How does this come about?
   • Where is the epipole when this happens?
5. Review the original exercise text. Does it make sense in terms of the thought experiment that you have just conducted?

Exercise 5.8

Given two images \(x_1\), \(x_2\) of a point \(p\) together with the relative camera motion \((R,T)\), \(\mathbf{X}_2=R\mathbf{X}_1+T\):

1. express the depth
2. express the depth

Exercise 5.9

Optional exercises

• Exercise 5.3
• Exercise 5.4
• Exercise 5.2 (1)

Debrief